Find the area of the minor segment of a circle of radius 42cm, if the length of the corresponding arc is 44 cm.
Answers
Answer:
160.0 cm²
Step-by-step explanation:
R = 42 cm; s = 44 cm
1. Central angle θ (working in radians)
θ = s/R
θ = 44/42
θ = 22/21
===============
2. Area of sector
A = ½R²θ
A = ½(42)²(22/21)
A = ½(42×21×2)(22/21)
A = 924 cm²
===============
3. Area of triangle
A = ½R²sinθ
A = ½(42)²sin(22/21)
A = ½ ×1764 × 0.8662
A = 764.0 cm²
===============
4. Area of segment
Area of segment = Area of sector – area of triangle
= 924 – 764.0
= 160.0 cm²
The area of segment is [tex]\boxed{160{\text{ c}}{{\text{m}}^2}}.[/tex]
Further explanation:
The formula of angle can be obtained as follows,
[tex]\boxed{\theta= \frac{{{\text{arc}}}}{{{\text{radius}}}}}[/tex]
The formula for area of sector can be expressed as follows,
[tex]\boxed{{\text{Area of sector}} = \frac{1}{2}{r^2}\theta }[/tex]
The formula for area of triangle can be expressed as follows,
[tex]\boxed{{\text{Area of triangle}} = \frac{1}{2}{r^2}\sin \theta }[/tex]
Given:
The radius of the circle is [tex]42{\text{ cm}}.[/tex]
The length of an arc is [tex]44{\text{ cm}}.[/tex]
Explanation:
The radius of the sector is [tex]42{\text{ cm}}[/tex] and the length of an arc is [tex]44{\text{ cm}}.[/tex]
The angle can be obtained as follows,
[tex]\begin{aligned}\theta&= \frac{l}{r}\\&=\frac{{44}}{{42}}\\&= \frac{{22}}{{21}}\\\end{aligned}[/tex]
Area of the triangle can be obtained as follows,
[tex]\begin{aligned}{\text{Area}}&= \frac{1}{2}{r^2}\sin {{\theta }}\\{\text{ }}=&\frac{1}{2}{\left( {42} \right)^2}\sin \left( {\frac{{22}}{{21}}} \right) \\&=882 \times 0.8662\\&=764{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
Area of sector can be obtained as follows,
[tex]\begin{aligned}A&= \frac{1}{2}{r^2}\theta\\&= \frac{1}{2} \times {\left( {42} \right)^2} \times \left({\frac{{22}}{{21}}} \right) \\&= 924{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of segment can be obtained as follows,
[tex]\begin{aligned}{\text{Area of segment}}&= {\text{Area of sector}} - {\text{Area of triangle}}\\&= {\text{924}} - 764\\&= 160{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of segment is [tex]\boxed{160{\text{ c}}{{\text{m}}^2}}.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Area of Circles
Keywords: area, minor segment, circle, radius 42 cm, length of the corresponding arc is 44 cm, sector, segment.
Related Questions
What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)
Answers
The remainder when the polynomial f(x) = 3x³ - 4x² + 2x + 8 is divided by (x - 5) is constant an equal f(5).
Substitute x = 5 to the polynomial:
[tex]f(5)=3(5^3)-4(5^2)+2(5)+8=3(125)-4(25)+10+8\\\\=375-100+18=275+18=293[/tex]
Answer: (3x³ - 4x² + 2x + 8) : (x - 5) = q(x) + 293.
The table shows the number of miles driven over time. Express the relationship between distance and time in simplified form as a unit rate.
Time (hours)
4
6
8
10
Distance (miles)
188
282
376
470
Answers
Answer:
Relationship between distance and time in simplified form as a unit rate is; [tex]\frac{47}{1}[/tex]
Step-by-step explanation:
Unit rate defined as the rates are expressed as a quantity of 1, such as 5 feet per second or 3 miles per hour, they are called unit rates.
Unit rate = [tex]\frac{distance}{time}[/tex]
From the given table:
Take any
time = 4 hours and distance= 188 miles
then, by definition of unit rate;
Unit rate = [tex]\frac{188}{4} =\frac{47}{1}[/tex]
Since, this is the constant rate.
Therefore, the relationship between distance and time in simplified form as a unit rate is; [tex]\frac{47}{1}[/tex]
parallelogram JSTP∼parallelogram BFMY
Drag the answers into the boxes to match each part of parallelogram JSTP with the corresponding part of parallelogram BFMY .
Answers
Answer:
[tex]\angle P=\angle Y;[/tex]
[tex]\overline {ST}[/tex] and [tex]\overline {FM};[/tex]
[tex]\angle T=\angle M;[/tex]
[tex]\overline {JP}[/tex] and [tex]\overline {BY}.[/tex]
Step-by-step explanation:
Similar figures have proportional corresponding sides and congruent corresponding angles. If parallelogram JSTP is similar to parallelogram BFMY, then
[tex]\angle J=\angle B;[/tex] [tex]\angle S=\angle F;[/tex][tex]\angle T=\angle M;[/tex][tex]\angle P=\angle Y;[/tex][tex]\dfrac{JS}{BF}=\dfrac{ST}{FM}=\dfrac{TP}{MY}=\dfrac{JT}{BM}=\dfrac{JP}{BY}=\dfrac{SP}{FY}.[/tex]Answer:
Step-by-step explanation:
p=y
by looking at the end of the angles you can tell that P is corresponding to y
ST=FM
since both are in the middle of their angles they are both considered a corresponding
T=M
both are the third within their angle there for corresponding
JP=BY
both are within the same place with therefore equal
3/4+7/12 adding and subtracting fractions with value
Answers
Answer:
1 1/3
Step-by-step explanation:
Change 3/4 to 9/12 and then add 9/12 and 7/12.
You get 16/12 and then simplify it by dividing it by 4.
4 lbs of onions cost $12. How many lbs of onions can you get with $147? PLEASE SHOW WORK....
Answers
Answer:
Step-by-step explanation:if is it 12 per. pound just divide 147 by 12 and you get your answer hope it was helpful
Answer:
49 lbs of onions
Step-by-step explanation:
147/12 = 12.25
12.25 x 4 = 49
A figure is dilated by a factor of 3. Which statement about measurements of image is ture
Answers
PLEASE HELP!!!!!!!!!30 POINTS!!!!!!!!!!!!!!!!!!!!PRETTY SIMPLE QUESTION!!!!!!!
Which correctly describes how the graph of the inequality −4y − x ≥ 7 is shaded?
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answers
Answer:
Below the solid line.
Step-by-step explanation:
When you solve for y, you will have a less than or equal to sign, so the shading is below the line.
Answer:
Below the solid line
Step-by-step explanation:
−4y − x ≥ 7
We need to solve for y
Add x to each side
−4y − x +x≥ 7+x
-4y ≥ 7+x
Divide each side by -4. Remember to flip the inequality
−4y/-4 ≤ (7+x)/-4
y ≤ -1/4 x - 7/4
Y is less than or equal to the value so the line is solid (equals sign)
and below ( less than)
Which are the x-intercepts of the graphed function?
Answers
Answer: the correct option is
(B) (-3, 0) and (1, 0).
Step-by-step explanation: We are given to find the x-intercepts of the graphed function.
We know that
x-intercepts of a function are the points on the X-axis through which the graph of the function is crossing.
From the graph, we see that
the curve is crossing the X-axis at the points (-3, 0) and (1, 0).
Therefore, the x-intercepts of the given function are (-3, 0) and (1, 0).
Option (B) is CORRECT.
CHECK MY WORK PLEASE AND ANSWER SOME QUESTION!!!!!!!! ASAP
WILL GIVE BRAINIEST
Which number is a solution of the inequality?
g > 6.4
A. 7***
B.6
C.6.4
D.-7
Which number is a solution of the inequality?
y+2>8
A. -5
B.-6
C.6***
D.7
Which number is a solution of the inequality? ( i need help with this one and on)
6>z(10-z)
A. 0
B.1
C.2
D.3
If N is the set of natural numbers that are factors of 24, choose the selection below that correctly shows this set in roster form.
A. {2, 4, 6, 12}
B. { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
C. { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}
D. { 1, 2, 3, 4, 6, 8, 12, 24}
Answers
1.
g > 6.4
Answer: A. 7 > 6.42.
y + 2 > 8 subtract 2 from both sides
y > 6
Answer: D. 7 > 63.
6 > z(10 - z)
A. z = 0 → 6 > 0(10 - 0) → 6 > 0 CORRECT
B. z = 1 → 6 > 1(10 - 1) → 6 > 1(9) → 6 > 9 FALSE
C. z = 2 → 6 > 2(10 - 2) → 6 > 2(8) → 6 > 16 FALSE
D. z = 3 → 6 > 3(10 - 3) → 6 > 3(7) → 6 > 21 FALSE
Answer: A. 04.
The list of factors of 24:
1, 24, 2, 12, 3, 8, 4, 6
Answer: D. {1, 2, 3, 4, 6, 8, 12, 24}830000 in scientific notation
Answers
Answer:
8.3 * 10 ^5
Step-by-step explanation:
830000
To change this to scientific notation, we move the decimal 5 places to the left. The exponent will be positive 5 because we moved it to the left
8.3 * 10^ +5
8.3 * 10 ^5
help me please help me
Answers
Answer:
1st=300,000 2nd=50
Step-by-step explanation:
Nate finishes his garden at 4:47 p. After pruning his roses for 18 minutes and watering his vegetables for 45 minutes. What time does Nate finish gardening?
Answers
How do I find the missing side for question 39
Answers
Hello from MrBillDoesMath!
Answer:
#39 6.1 (approx)
$41 14.6 (approx)
Discussion:
# 39
From plane trigonometry
cos(69) = x/17 or
x = 17 * cos(69) = 6.1 (approx)
#41
sin(59) = x/17 or
x = 17 * sin(59) = 14.6 (approx)
Regards,
MrB
Beanbag chairs it normally sell for $36.30 on sale for $32.12 find the percent of discount
Answers
Answer:
Step-by-step explanation:
What is the LARGEST number of real zeros a polynomial with degree n can have?
Answers
Answer:
n
Step-by-step explanation:
The zeros of the function are the x-intercepts of the function. They can be real or imaginary. The most a polynomial can have is its degree. If the degree is n then there can be n amount.
Caleb is 4 times Jessica's age Jessica is twice Noah's age Noah is one year older than Mary Mary is 3 yrs old how old is Caleb
Answers
someone halp what 1+1 idk eee
Answers
Answer:
2
Step-by-step explanation:
Answer: 1+1 =2
Step-by-step explanation: If you add 1 plus another 1 you would just have to add and you will find 2.
Carlos writes 1/8 of a page in 1/2 of a minute. How many pages will he have written in one minute?
Answers
Answer:
1/4 pages
Step-by-step explanation:
1/8 page in 1/2 minutes
X number of pages in 1 minute
Answer:
2/8
Step-by-step explanation:
Since 1/2 a minute is 1/8 of a page. One full minute would mean another 1/2, so that means we need another 1/8, and 1/8 + 1/8= 2/8
You spent z dollars today. Today, you spent 5.5 times as many dollars as you spent yesterday. Which expression correctly shows how much you spent yesterday?

5.5z

5.5 ÷ z

5.5(1 − z)

z ÷ 5.5

none of the above
Answers
Answer:
Z ÷ 5.5
Step-by-step explanation:
The correct expression to show how much was spent yesterday when z dollars were spent today and that amount is 5.5 * the spending of yesterday is z divided by 5.5. The correct answer is option (D) z ÷ 5.5.
If you spent z dollars today and that amount is 5.5 * what you spent yesterday, to find out how much you spent yesterday, you would divide the amount spent today by 5.5. This is because the relationship between what was spent today (z dollars) and what was spent yesterday is multiplicative. Today’s spending (z) is equal to 5.5 * yesterday’s spending, so to find out what you spent yesterday, you would express it as z divided by 5.5.
Thus, the correct answer to the student's question is option (D) z ÷ 5.5.
i need help with these problems please show your work
Answers
9.)
The image of point (-6, 2) after a 90° counterclockwise rotation is (-2, -6). This is because a 90° counterclockwise rotation is the same as a 270° clockwise rotation, which is (x, y) → (-y, x).
10.)
The image of point (-9, 3) after reflective it over the line y = x is (3, -9). This is because a reflection over the line y = x is (x, y) → (y, x).
11.)
The blank is "rigid" because rigid transformations preserve length.
PLEASE HELP ME! 44 points and will mark brainliestttt
The graphed line shown below is Y=-2X-8
Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?
A Y=--(2X+8)
B y= -(2x-8)
C y=-2 (x-4)
D y= -(-2x+8)
Answers
Answer:
a
Step-by-step explanation:
no need
74.362 to the nearest tenth
Answers
Answer:
73.4
Step-by-step explanation:
When they ask for the nearest tenth you check the hundreth, it its 5 or ore than you increase the tenth
The number 74.362 would round down to 74.4
For Rounding some number to a specific value is making its value simpler mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of trimmed from the right in terms of exact digits.
We need to round 74.362 to the nearest tenth,
To round 74.362 to the nearest tenth, we need to look at the digit in the hundredth place, which is 2. Since 2 is less than 5, we round down and keep 4.
Therefore, rounding 74.362 to the nearest tenth gives us 74.4.
Learn more about rounding numbers here:
brainly.com/question/1285054
#SPJ6
two angles in a triangle mesaure 65 degrees and 75 degrees what is the measure of the third angle of the triangle
Answers
Answer:
40°
Step-by-step explanation:
The interior sum of a triangle is 180°. Since we have two known angles we will subtract those values from 180 to obtain our third angle and so:
180°-65°-75°=40°
Answer:
Not sure but i think its 45°.
Step-by-step explanation:
prove the angle sum property of a triangle
Answers
Answer:
ANGLE SUM PROPERTY OF A TRIANGLEStep-by-step explanation:
PROPERTY 1 : Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
PROOF : Draw a triangle , then mark each angle as A , B , and C . then take a compass and mark three ark in three sides of a triangle and cut the angles of B and C , then join the two angle B and C with angle A . Then you will find there a COMPLETE ANGLE .
The sum of the measures of angles of triangle is equal 180°.
Look at the picture.
We have the congruent corresponding angles and the vertical angles.
[tex]100 \div 100 = 1000[/tex]
right or wrong
Answers
Answer:
Wrong
Step-by-step explanation:
100 divided by 100 would simply be equal to one.
If you had 100 things and split it into 100 groups, you'd have 100 groups of just one single thing.
Answer:
false
Step-by-step explanation:
100÷ 100 = 1000
100/100 = 1
You are dividing something by itself.
Something divided by itself is 1
General conic equation
Answers
There are 3 types of conics: parabola, ellipse, and hyperbola.
Equation of a parabola: y = a(x - h)² + k or x = a(y - k)² + h
Equation of an ellipse: [tex]\frac{(x-h)^{2}}{a} +\frac{(y-k)^{2}}{b} =1[/tex]
Equation of a hyperbola: [tex]\frac{(x-h)^{2}}{a} -\frac{(y-k)^{2}}{b} =1[/tex]
The general equation for all of them is:
Ax² + Bxy + Cy² + Dx + Ey + F = 0 ; A, B, C, D, E, F ∈ Integers
WILL MARK BRAINLIEST!!! : ) Need an answer now! Thanks
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.
Which graph represents this wage increase for x < 12?
Answers
Answer:
I think it's the third!
Step-by-step explanation:
Answer:
The answer is the 3rd one : )
i need help thx so much
Answers
Answer:
$40.51
Step-by-step explanation:
sales tax = original price * tax rate
tax rate = 10 percent = .10
sales tax = 405.10 * .1
= 40.51
what is the square root of 850
Answers
Alan has an annual base salary of $24,000. In addition to his salary, he earns 8% of his total sales (S). If he wants to earn at least $56,000 next year, how much does he need to sell?
A. S > $244,480
B. S > $550,000
C. S > $448,000
D. S > $400,000
Answers
Answer:
D. S > $400,000
Step-by-step explanation:
His salary is base salary plus commission
salary = 24000 + .08 sales
He wants a salary of at least 56000
56000<= 24000 +.08 sales
Subtract 24000
56000-24000<= 24000-24000+.08*sales
32000<= .08 * sales
Divide each side by .08
32000/.08 <= .08/.08 * sales
400000<= sales